I switched my 65 Cutlass to internal regulator...nothing fancy..just a little newer three wire. It came prewired in my new M&H wiring as an upgrade.
My alternator light is on dim all the time while the car is running...It runs fine and the only only problem is the gas guage needle bouncing around sometimes... I had this proplem once before about 30 yrs ago when I did the same swap...dont recall what I did about it...

 

I had it happen too - it is a 1 wire alt most likely - unplug the white plastic terminal / connector and leave just the single red lead connected

 

So the while plug on top does nothing? Other than the bulb being on and eventually burning out what else is happening if it stays plugged in...

 

I wouldn't pay a dime for a one wire alternator, they cause more problems than they solve. If the alt light is on dim with the engine running then chances are you have a bad diode in the alt. easy and cheap fix.

 

Check for a bad ground on the cluster just put a jumper wire onto the case of the cluster and see what happens...

 

It was a bad ground...had checked and cleaned them before but not good enough...probably the same reason my power window switch smoked for a sec last night !! @%$#@ grounds...

 

The GEN light circuit does not ground in the instrument panel. The bulb is supplied with +12v with the key in the RUN position. The other side of the bulb is connected to the #1 terminal on the alternator (assuming a three wire, internal regulator alt, like the SI-family). In the regulator, the #1 terminal is grounded when the alt output is low and should be full alt voltage when the alt is charging. By having the same voltage on both sides of the bulb, it does not illuminate. If voltage on one side (and it could be either side) is low, current flows through the filament and the bulb starts to glow. The greater the voltage differential, the brighter the bulb. If the bulb is glowing dimly, you have a voltage drop on one side of the bulb. Start by checking output voltage at the #1 terminal on the alternator - it should be 13.8V or so. If you can get to the IP connector or the two terminals of the bulb socket, check the voltage of each of those to ground with the engine running. They should be the same. If one is lower, find the voltage drop in that wire. It will likely be a dirty connector terminal someplace.